Optimization Design for Spur Gear with Stress-Relieving Holes

Abstract

By designing stress-relieving holes in the stressed zone, an optimization design for reduction of root fillet stress in spur gear is presented based on the stress redistribution techniques. The design method consists of two parts as follows. In the first part, a finite element model that is combined with two gear segments for pinion gear and driven gear is built and the bending stress is analyzed. In the second part, the sizes and the locations of the stress-relieving holes of the gear teeth are optimized in order to reduce the root fillet stress. In the procedures of optimization design, the numerical simulation results by using Ansys Workbench are first used to construct the metamodels which can reduce the computational cost of the finite element analysis (FEA). In the metamodeling process, the optimal Space-Filling design (SFD) method is employed for the selection of sampling design points in design space, and the polynomial response surface (PRS) is utilized to formulate the design objective σmax. Based on the metamodels of the design objective, the genetic algorithm (GA) methodology is employed to find out the optimized locations and sizes of the holes at the root fillet. An illustrated example shows that the maximum principal stress in gear root fillet has been reduced by 14.69% based on the proposed optimization design. This implies the feasibility of the optimization design for increasing the life of gear by designing stress-relieving holes.